tests/suites/test_suite_mpi.function

/* BEGIN_HEADER */
#include "mbedtls/bignum.h"
#include "mbedtls/entropy.h"
#include "bignum_core.h"
#include "bignum_mod.h"
#include "bignum_mod_raw.h"
#include "constant_time_internal.h"
#include "test/constant_flow.h"

#if MBEDTLS_MPI_MAX_BITS > 792
#define MPI_MAX_BITS_LARGER_THAN_792
#endif

/* Check the validity of the sign bit in an MPI object. Reject representations
 * that are not supported by the rest of the library and indicate a bug when
 * constructing the value. */
static int sign_is_valid( const mbedtls_mpi *X )
{
    if( X->s != 1 && X->s != -1 )
        return( 0 ); // invalid sign bit, e.g. 0
    if( mbedtls_mpi_bitlen( X ) == 0 && X->s != 1 )
        return( 0 ); // negative zero
    return( 1 );
}

typedef struct mbedtls_test_mpi_random
{
    data_t *data;
    size_t  pos;
    size_t  chunk_len;
} mbedtls_test_mpi_random;

/*
 * This function is called by the Miller-Rabin primality test each time it
 * chooses a random witness. The witnesses (or non-witnesses as provided by the
 * test) are stored in the data member of the state structure. Each number is in
 * the format that mbedtls_mpi_read_string understands and is chunk_len long.
 */
int mbedtls_test_mpi_miller_rabin_determinizer( void* state,
                                                unsigned char* buf,
                                                size_t len )
{
    mbedtls_test_mpi_random *random = (mbedtls_test_mpi_random*) state;

    if( random == NULL || random->data->x == NULL || buf == NULL )
        return( -1 );

    if( random->pos + random->chunk_len > random->data->len
            || random->chunk_len > len )
    {
        return( -1 );
    }

    memset( buf, 0, len );

    /* The witness is written to the end of the buffer, since the buffer is
     * used as big endian, unsigned binary data in mbedtls_mpi_read_binary.
     * Writing the witness to the start of the buffer would result in the
     * buffer being 'witness 000...000', which would be treated as
     * witness * 2^n for some n. */
    memcpy( buf + len - random->chunk_len, &random->data->x[random->pos],
            random->chunk_len );

    random->pos += random->chunk_len;

    return( 0 );
}

/* Random generator that is told how many bytes to return. */
static int f_rng_bytes_left( void *state, unsigned char *buf, size_t len )
{
    size_t *bytes_left = state;
    size_t i;
    for( i = 0; i < len; i++ )
    {
        if( *bytes_left == 0 )
            return( MBEDTLS_ERR_ENTROPY_SOURCE_FAILED );
        buf[i] = *bytes_left & 0xff;
        --( *bytes_left );
    }
    return( 0 );
}

/* Test whether bytes represents (in big-endian base 256) a number b that
 * is significantly above a power of 2. That is, b must not have a long run
 * of unset bits after the most significant bit.
 *
 * Let n be the bit-size of b, i.e. the integer such that 2^n <= b < 2^{n+1}.
 * This function returns 1 if, when drawing a number between 0 and b,
 * the probability that this number is at least 2^n is not negligible.
 * This probability is (b - 2^n) / b and this function checks that this
 * number is above some threshold A. The threshold value is heuristic and
 * based on the needs of mpi_random_many().
 */
static int is_significantly_above_a_power_of_2( data_t *bytes )
{
    const uint8_t *p = bytes->x;
    size_t len = bytes->len;
    unsigned x;

    /* Skip leading null bytes */
    while( len > 0 && p[0] == 0 )
    {
        ++p;
        --len;
    }
    /* 0 is not significantly above a power of 2 */
    if( len == 0 )
        return( 0 );
    /* Extract the (up to) 2 most significant bytes */
    if( len == 1 )
        x = p[0];
    else
        x = ( p[0] << 8 ) | p[1];

    /* Shift the most significant bit of x to position 8 and mask it out */
    while( ( x & 0xfe00 ) != 0 )
        x >>= 1;
    x &= 0x00ff;

    /* At this point, x = floor((b - 2^n) / 2^(n-8)). b is significantly above
     * a power of 2 iff x is significantly above 0 compared to 2^8.
     * Testing x >= 2^4 amounts to picking A = 1/16 in the function
     * description above. */
    return( x >= 0x10 );
}

/* END_HEADER */

/* BEGIN_DEPENDENCIES
 * depends_on:MBEDTLS_BIGNUM_C
 * END_DEPENDENCIES
 */

/* BEGIN_CASE */
void mpi_null(  )
{
    mbedtls_mpi X, Y, Z;

    mbedtls_mpi_init( &X );
    mbedtls_mpi_init( &Y );
    mbedtls_mpi_init( &Z );

    TEST_ASSERT( mbedtls_mpi_get_bit( &X, 42 ) == 0 );
    TEST_ASSERT( mbedtls_mpi_lsb( &X ) == 0 );
    TEST_ASSERT( mbedtls_mpi_bitlen( &X ) == 0 );
    TEST_ASSERT( mbedtls_mpi_size( &X ) == 0 );

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_read_write_string( int radix_X, char * input_X, int radix_A,
                            char * input_A, int output_size, int result_read,
                            int result_write )
{
    mbedtls_mpi X;
    char str[1000];
    size_t len;

    mbedtls_mpi_init( &X );

    memset( str, '!', sizeof( str ) );

    TEST_ASSERT( mbedtls_mpi_read_string( &X, radix_X, input_X ) == result_read );
    if( result_read == 0 )
    {
        TEST_ASSERT( sign_is_valid( &X ) );
        TEST_ASSERT( mbedtls_mpi_write_string( &X, radix_A, str, output_size, &len ) == result_write );
        if( result_write == 0 )
        {
            TEST_ASSERT( strcasecmp( str, input_A ) == 0 );
            TEST_ASSERT( str[len] == '!' );
        }
    }

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_read_binary( data_t * buf, char * input_A )
{
    mbedtls_mpi X;
    char str[1000];
    size_t len;

    mbedtls_mpi_init( &X );


    TEST_ASSERT( mbedtls_mpi_read_binary( &X, buf->x, buf->len ) == 0 );
    TEST_ASSERT( sign_is_valid( &X ) );
    TEST_ASSERT( mbedtls_mpi_write_string( &X, 16, str, sizeof( str ), &len ) == 0 );
    TEST_ASSERT( strcmp( (char *) str, input_A ) == 0 );

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_io_null()
{
    mbedtls_mpi_uint X = 0;
    int ret;

    ret = mbedtls_mpi_core_read_be( &X, 1, NULL, 0 );
    TEST_EQUAL( ret, 0 );
    ret = mbedtls_mpi_core_write_be( &X, 1, NULL, 0 );
    TEST_EQUAL( ret, 0 );

    ret = mbedtls_mpi_core_read_be( NULL, 0, NULL, 0 );
    TEST_EQUAL( ret, 0 );
    ret = mbedtls_mpi_core_write_be( NULL, 0, NULL, 0 );
    TEST_EQUAL( ret, 0 );

    ret = mbedtls_mpi_core_read_le( &X, 1, NULL, 0 );
    TEST_EQUAL( ret, 0 );
    ret = mbedtls_mpi_core_write_le( &X, 1, NULL, 0 );
    TEST_EQUAL( ret, 0 );

    ret = mbedtls_mpi_core_read_le( NULL, 0, NULL, 0 );
    TEST_EQUAL( ret, 0 );
    ret = mbedtls_mpi_core_write_le( NULL, 0, NULL, 0 );
    TEST_EQUAL( ret, 0 );

exit:
    ;
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_io_be( data_t *input, int nb_int, int nx_32_int, int iret,
                     int oret )
{
    if( iret != 0 )
        TEST_ASSERT( oret == 0 );

    TEST_LE_S( 0, nb_int );
    size_t nb = nb_int;

    unsigned char buf[1024];
    TEST_LE_U( nb, sizeof( buf ) );

    /* nx_32_int is the number of 32 bit limbs, if we have 64 bit limbs we need
     * to halve the number of limbs to have the same size. */
    size_t nx;
    TEST_LE_S( 0, nx_32_int );
    if( sizeof( mbedtls_mpi_uint ) == 8 )
        nx = nx_32_int / 2 + nx_32_int % 2;
    else
        nx = nx_32_int;

    mbedtls_mpi_uint X[sizeof( buf ) / sizeof( mbedtls_mpi_uint )];
    TEST_LE_U( nx, sizeof( X ) / sizeof( X[0] ) );

    int ret = mbedtls_mpi_core_read_be( X, nx, input->x, input->len );
    TEST_EQUAL( ret, iret );

    if( iret == 0 )
    {
        ret =  mbedtls_mpi_core_write_be( X, nx, buf, nb );
        TEST_EQUAL( ret, oret );
    }

    if( ( iret == 0 ) && ( oret == 0 ) )
    {
        if( nb > input->len )
        {
            size_t leading_zeroes = nb - input->len;
            TEST_ASSERT( memcmp( buf + nb - input->len, input->x, input->len ) == 0 );
            for( size_t i = 0; i < leading_zeroes; i++ )
                TEST_EQUAL( buf[i], 0 );
        }
        else
        {
            size_t leading_zeroes = input->len - nb;
            TEST_ASSERT( memcmp( input->x + input->len - nb, buf, nb ) == 0 );
            for( size_t i = 0; i < leading_zeroes; i++ )
                TEST_EQUAL( input->x[i], 0 );
        }
    }

exit:
    ;
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_io_le( data_t *input, int nb_int, int nx_32_int, int iret,
                     int oret )
{
    if( iret != 0 )
        TEST_ASSERT( oret == 0 );

    TEST_LE_S( 0, nb_int );
    size_t nb = nb_int;

    unsigned char buf[1024];
    TEST_LE_U( nb, sizeof( buf ) );

    /* nx_32_int is the number of 32 bit limbs, if we have 64 bit limbs we need
     * to halve the number of limbs to have the same size. */
    size_t nx;
    TEST_LE_S( 0, nx_32_int );
    if( sizeof( mbedtls_mpi_uint ) == 8 )
        nx = nx_32_int / 2 + nx_32_int % 2;
    else
        nx = nx_32_int;

    mbedtls_mpi_uint X[sizeof( buf ) / sizeof( mbedtls_mpi_uint )];
    TEST_LE_U( nx, sizeof( X ) / sizeof( X[0] ) );

    int ret =  mbedtls_mpi_core_read_le( X, nx, input->x, input->len );
    TEST_EQUAL( ret, iret );

    if( iret == 0 )
    {
        ret =  mbedtls_mpi_core_write_le( X, nx, buf, nb );
        TEST_EQUAL( ret, oret );
    }

    if( ( iret == 0 ) && ( oret == 0 ) )
    {
        if( nb > input->len )
        {
            TEST_ASSERT( memcmp( buf, input->x, input->len ) == 0 );
            for( size_t i = input->len; i < nb; i++ )
                TEST_EQUAL( buf[i], 0 );
        }
        else
        {
            TEST_ASSERT( memcmp( input->x, buf, nb ) == 0 );
            for( size_t i = nb; i < input->len; i++ )
                TEST_EQUAL( input->x[i], 0 );
        }
    }

exit:
    ;
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_mod_setup( int ext_rep, int int_rep, int iret )
{
    #define MLIMBS 8
    mbedtls_mpi_uint mp[MLIMBS];
    mbedtls_mpi_mod_modulus m;
    int ret;

    memset( mp, 0xFF, sizeof(mp) );

    mbedtls_mpi_mod_modulus_init( &m );
    ret = mbedtls_mpi_mod_modulus_setup( &m, mp, MLIMBS, ext_rep, int_rep );
    TEST_EQUAL( ret, iret );

    /* Address sanitiser should catch if we try to free mp */
    mbedtls_mpi_mod_modulus_free( &m );

    /* Make sure that the modulus doesn't have reference to mp anymore */
    TEST_ASSERT( m.p != mp );

exit:
    /* It should be safe to call an mbedtls free several times */
    mbedtls_mpi_mod_modulus_free( &m );

    #undef MLIMBS
}
/* END_CASE */


/* BEGIN_CASE */
void mpi_mod_raw_io( data_t *input, int nb_int, int nx_32_int,
                     int iendian, int iret, int oret )
{
    if( iret != 0 )
        TEST_ASSERT( oret == 0 );

    TEST_LE_S( 0, nb_int );
    size_t nb = nb_int;

    unsigned char buf[1024];
    TEST_LE_U( nb, sizeof( buf ) );

    /* nx_32_int is the number of 32 bit limbs, if we have 64 bit limbs we need
     * to halve the number of limbs to have the same size. */
    size_t nx;
    TEST_LE_S( 0, nx_32_int );
    if( sizeof( mbedtls_mpi_uint ) == 8 )
        nx = nx_32_int / 2 + nx_32_int % 2;
    else
        nx = nx_32_int;

    mbedtls_mpi_uint X[sizeof( buf ) / sizeof( mbedtls_mpi_uint )];
    TEST_LE_U( nx, sizeof( X ) / sizeof( X[0] ) );

    int endian;
    if( iendian == MBEDTLS_MPI_MOD_EXT_REP_INVALID )
        endian = MBEDTLS_MPI_MOD_EXT_REP_LE;
    else
        endian = iendian;

    mbedtls_mpi_mod_modulus m;
    mbedtls_mpi_mod_modulus_init( &m );
    mbedtls_mpi_uint init[sizeof( X ) / sizeof( X[0] )];
    memset( init, 0xFF, sizeof( init ) );
    int ret = mbedtls_mpi_mod_modulus_setup( &m, init, nx, endian,
                                             MBEDTLS_MPI_MOD_REP_MONTGOMERY );
    TEST_EQUAL( ret, 0 );

    if( iendian == MBEDTLS_MPI_MOD_EXT_REP_INVALID && iret != 0 )
        m.ext_rep = MBEDTLS_MPI_MOD_EXT_REP_INVALID;

    ret = mbedtls_mpi_mod_raw_read( X, &m, input->x, input->len );
    TEST_EQUAL( ret, iret );

    if( iret == 0 )
    {
        if( iendian == MBEDTLS_MPI_MOD_EXT_REP_INVALID && oret != 0 )
            m.ext_rep = MBEDTLS_MPI_MOD_EXT_REP_INVALID;

        ret = mbedtls_mpi_mod_raw_write( X, &m, buf, nb );
        TEST_EQUAL( ret, oret );
    }

    if( ( iret == 0 ) && ( oret == 0 ) )
    {
        if( nb > input->len )
        {
            if( endian == MBEDTLS_MPI_MOD_EXT_REP_BE )
            {
                size_t leading_zeroes = nb - input->len;
                TEST_ASSERT( memcmp( buf + nb - input->len, input->x, input->len ) == 0 );
                for( size_t i = 0; i < leading_zeroes; i++ )
                    TEST_EQUAL( buf[i], 0 );
            }
            else
            {
                TEST_ASSERT( memcmp( buf, input->x, input->len ) == 0 );
                for( size_t i = input->len; i < nb; i++ )
                    TEST_EQUAL( buf[i], 0 );
            }
        }
        else
        {
            if( endian == MBEDTLS_MPI_MOD_EXT_REP_BE )
            {
                size_t leading_zeroes = input->len - nb;
                TEST_ASSERT( memcmp( input->x + input->len - nb, buf, nb ) == 0 );
                for( size_t i = 0; i < leading_zeroes; i++ )
                    TEST_EQUAL( input->x[i], 0 );
            }
            else
            {
                TEST_ASSERT( memcmp( input->x, buf, nb ) == 0 );
                for( size_t i = nb; i < input->len; i++ )
                    TEST_EQUAL( input->x[i], 0 );
            }
        }
    }

exit:
    mbedtls_mpi_mod_modulus_free( &m );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_read_binary_le( data_t * buf, char * input_A )
{
    mbedtls_mpi X;
    char str[1000];
    size_t len;

    mbedtls_mpi_init( &X );


    TEST_ASSERT( mbedtls_mpi_read_binary_le( &X, buf->x, buf->len ) == 0 );
    TEST_ASSERT( sign_is_valid( &X ) );
    TEST_ASSERT( mbedtls_mpi_write_string( &X, 16, str, sizeof( str ), &len ) == 0 );
    TEST_ASSERT( strcmp( (char *) str, input_A ) == 0 );

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_write_binary( char * input_X, data_t * input_A,
                       int output_size, int result )
{
    mbedtls_mpi X;
    unsigned char buf[1000];
    size_t buflen;

    memset( buf, 0x00, 1000 );

    mbedtls_mpi_init( &X );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );

    buflen = mbedtls_mpi_size( &X );
    if( buflen > (size_t) output_size )
        buflen = (size_t) output_size;

    TEST_ASSERT( mbedtls_mpi_write_binary( &X, buf, buflen ) == result );
    if( result == 0)
    {

        TEST_ASSERT( mbedtls_test_hexcmp( buf, input_A->x,
                                          buflen, input_A->len ) == 0 );
    }

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_write_binary_le( char * input_X, data_t * input_A,
                          int output_size, int result )
{
    mbedtls_mpi X;
    unsigned char buf[1000];
    size_t buflen;

    memset( buf, 0x00, 1000 );

    mbedtls_mpi_init( &X );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );

    buflen = mbedtls_mpi_size( &X );
    if( buflen > (size_t) output_size )
        buflen = (size_t) output_size;

    TEST_ASSERT( mbedtls_mpi_write_binary_le( &X, buf, buflen ) == result );
    if( result == 0)
    {

        TEST_ASSERT( mbedtls_test_hexcmp( buf, input_A->x,
                                          buflen, input_A->len ) == 0 );
    }

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE depends_on:MBEDTLS_FS_IO */
void mpi_read_file( char * input_file, data_t * input_A, int result )
{
    mbedtls_mpi X;
    unsigned char buf[1000];
    size_t buflen;
    FILE *file;
    int ret;

    memset( buf, 0x00, 1000 );

    mbedtls_mpi_init( &X );

    file = fopen( input_file, "r" );
    TEST_ASSERT( file != NULL );
    ret = mbedtls_mpi_read_file( &X, 16, file );
    fclose(file);
    TEST_ASSERT( ret == result );

    if( result == 0 )
    {
        TEST_ASSERT( sign_is_valid( &X ) );
        buflen = mbedtls_mpi_size( &X );
        TEST_ASSERT( mbedtls_mpi_write_binary( &X, buf, buflen ) == 0 );


        TEST_ASSERT( mbedtls_test_hexcmp( buf, input_A->x,
                                          buflen, input_A->len ) == 0 );
    }

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE depends_on:MBEDTLS_FS_IO */
void mpi_write_file( char * input_X, char * output_file )
{
    mbedtls_mpi X, Y;
    FILE *file_out, *file_in;
    int ret;

    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );

    file_out = fopen( output_file, "w" );
    TEST_ASSERT( file_out != NULL );
    ret = mbedtls_mpi_write_file( NULL, &X, 16, file_out );
    fclose(file_out);
    TEST_ASSERT( ret == 0 );

    file_in = fopen( output_file, "r" );
    TEST_ASSERT( file_in != NULL );
    ret = mbedtls_mpi_read_file( &Y, 16, file_in );
    fclose(file_in);
    TEST_ASSERT( ret == 0 );

    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &Y ) == 0 );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_get_bit( char * input_X, int pos, int val )
{
    mbedtls_mpi X;
    mbedtls_mpi_init( &X );
    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_mpi_get_bit( &X, pos ) == val );

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_set_bit( char * input_X, int pos, int val,
                  char * output_Y, int result )
{
    mbedtls_mpi X, Y;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y, output_Y ) == 0 );
    TEST_ASSERT( mbedtls_mpi_set_bit( &X, pos, val ) == result );

    if( result == 0 )
    {
        TEST_ASSERT( sign_is_valid( &X ) );
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &Y ) == 0 );
    }

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_lsb( char * input_X, int nr_bits )
{
    mbedtls_mpi X;
    mbedtls_mpi_init( &X );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_mpi_lsb( &X ) == (size_t) nr_bits );

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_bitlen( char * input_X, int nr_bits )
{
    mbedtls_mpi X;
    mbedtls_mpi_init( &X );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_mpi_bitlen( &X ) == (size_t) nr_bits );

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_gcd( char * input_X, char * input_Y,
              char * input_A )
{
    mbedtls_mpi A, X, Y, Z;
    mbedtls_mpi_init( &A ); mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y, input_Y ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    TEST_ASSERT( mbedtls_mpi_gcd( &Z, &X, &Y ) == 0 );
    TEST_ASSERT( sign_is_valid( &Z ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Z, &A ) == 0 );

exit:
    mbedtls_mpi_free( &A ); mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_cmp_int( int input_X, int input_A, int result_CMP )
{
    mbedtls_mpi X;
    mbedtls_mpi_init( &X  );

    TEST_ASSERT( mbedtls_mpi_lset( &X, input_X ) == 0);
    TEST_ASSERT( mbedtls_mpi_cmp_int( &X, input_A ) == result_CMP);

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_cmp_mpi( char * input_X, char * input_Y,
                  int input_A )
{
    mbedtls_mpi X, Y;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y, input_Y ) == 0 );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &Y ) == input_A );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_lt_ct( data_t * input_X, data_t * input_Y, int input_ret )
{
    #define MAX_LEN 64
    mbedtls_mpi_uint X[MAX_LEN];
    mbedtls_mpi_uint Y[MAX_LEN];
    unsigned exp_ret = input_ret;
    unsigned ret;
    size_t len = CHARS_TO_LIMBS(
                    input_X->len > input_Y->len ? input_X->len : input_Y->len );

    TEST_LE_U( len, MAX_LEN );

    TEST_ASSERT( mbedtls_mpi_core_read_be( X, len, input_X->x, input_X->len )
                 == 0 );
    TEST_ASSERT( mbedtls_mpi_core_read_be( Y, len, input_Y->x, input_Y->len )
                 == 0 );

    TEST_CF_SECRET( X, len * sizeof( mbedtls_mpi_uint ) );
    TEST_CF_SECRET( Y, len * sizeof( mbedtls_mpi_uint ) );

    ret = mbedtls_mpi_core_lt_ct( X, Y, len );

    TEST_CF_PUBLIC( X, len * sizeof( mbedtls_mpi_uint ) );
    TEST_CF_PUBLIC( Y, len * sizeof( mbedtls_mpi_uint ) );
    TEST_CF_PUBLIC( &ret, sizeof( ret ) );

    TEST_EQUAL( ret, exp_ret );

exit:
    ;

    #undef MAX_LEN
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_lt_mpi_ct( int size_X, char * input_X,
                    int size_Y, char * input_Y,
                    int input_ret, int input_err )
{
    unsigned ret = -1;
    unsigned input_uret = input_ret;
    mbedtls_mpi X, Y;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y, input_Y ) == 0 );

    TEST_ASSERT( mbedtls_mpi_grow( &X, size_X ) == 0 );
    TEST_ASSERT( mbedtls_mpi_grow( &Y, size_Y ) == 0 );

    TEST_ASSERT( mbedtls_mpi_lt_mpi_ct( &X, &Y, &ret ) == input_err );
    if( input_err == 0 )
        TEST_ASSERT( ret == input_uret );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_cmp_abs( char * input_X, char * input_Y,
                  int input_A )
{
    mbedtls_mpi X, Y;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y, input_Y ) == 0 );
    TEST_ASSERT( mbedtls_mpi_cmp_abs( &X, &Y ) == input_A );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_copy( char *src_hex, char *dst_hex )
{
    mbedtls_mpi src, dst, ref;
    mbedtls_mpi_init( &src );
    mbedtls_mpi_init( &dst );
    mbedtls_mpi_init( &ref );

    TEST_ASSERT( mbedtls_test_read_mpi( &src, src_hex ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &ref, dst_hex ) == 0 );

    /* mbedtls_mpi_copy() */
    TEST_ASSERT( mbedtls_test_read_mpi( &dst, dst_hex ) == 0 );
    TEST_ASSERT( mbedtls_mpi_copy( &dst, &src ) == 0 );
    TEST_ASSERT( sign_is_valid( &dst ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &dst, &src ) == 0 );

    /* mbedtls_mpi_safe_cond_assign(), assignment done */
    mbedtls_mpi_free( &dst );
    TEST_ASSERT( mbedtls_test_read_mpi( &dst, dst_hex ) == 0 );
    TEST_ASSERT( mbedtls_mpi_safe_cond_assign( &dst, &src, 1 ) == 0 );
    TEST_ASSERT( sign_is_valid( &dst ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &dst, &src ) == 0 );

    /* mbedtls_mpi_safe_cond_assign(), assignment not done */
    mbedtls_mpi_free( &dst );
    TEST_ASSERT( mbedtls_test_read_mpi( &dst, dst_hex ) == 0 );
    TEST_ASSERT( mbedtls_mpi_safe_cond_assign( &dst, &src, 0 ) == 0 );
    TEST_ASSERT( sign_is_valid( &dst ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &dst, &ref ) == 0 );

exit:
    mbedtls_mpi_free( &src );
    mbedtls_mpi_free( &dst );
    mbedtls_mpi_free( &ref );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_copy_self( char *input_X )
{
    mbedtls_mpi X, A;
    mbedtls_mpi_init( &A );
    mbedtls_mpi_init( &X );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_mpi_copy( &X, &X ) == 0 );

    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_X ) == 0 );
    TEST_ASSERT( sign_is_valid( &X ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &A ) == 0 );

exit:
    mbedtls_mpi_free( &A );
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_swap( char *X_hex, char *Y_hex )
{
    mbedtls_mpi X, Y, X0, Y0;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y );
    mbedtls_mpi_init( &X0 ); mbedtls_mpi_init( &Y0 );

    TEST_ASSERT( mbedtls_test_read_mpi( &X0, X_hex ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y0, Y_hex ) == 0 );

    /* mbedtls_mpi_swap() */
    TEST_ASSERT( mbedtls_test_read_mpi( &X,  X_hex ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y,  Y_hex ) == 0 );
    mbedtls_mpi_swap( &X, &Y );
    TEST_ASSERT( sign_is_valid( &X ) );
    TEST_ASSERT( sign_is_valid( &Y ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &Y0 ) == 0 );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Y, &X0 ) == 0 );

    /* mbedtls_mpi_safe_cond_swap(), swap done */
    mbedtls_mpi_free( &X );
    mbedtls_mpi_free( &Y );
    TEST_ASSERT( mbedtls_test_read_mpi( &X,  X_hex ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y,  Y_hex ) == 0 );
    TEST_ASSERT( mbedtls_mpi_safe_cond_swap( &X, &Y, 1 ) == 0 );
    TEST_ASSERT( sign_is_valid( &X ) );
    TEST_ASSERT( sign_is_valid( &Y ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &Y0 ) == 0 );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Y, &X0 ) == 0 );

    /* mbedtls_mpi_safe_cond_swap(), swap not done */
    mbedtls_mpi_free( &X );
    mbedtls_mpi_free( &Y );
    TEST_ASSERT( mbedtls_test_read_mpi( &X,  X_hex ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y,  Y_hex ) == 0 );
    TEST_ASSERT( mbedtls_mpi_safe_cond_swap( &X, &Y, 0 ) == 0 );
    TEST_ASSERT( sign_is_valid( &X ) );
    TEST_ASSERT( sign_is_valid( &Y ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &X0 ) == 0 );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Y, &Y0 ) == 0 );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y );
    mbedtls_mpi_free( &X0 ); mbedtls_mpi_free( &Y0 );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_swap_self( char *X_hex )
{
    mbedtls_mpi X, X0;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &X0 );

    TEST_ASSERT( mbedtls_test_read_mpi( &X,  X_hex ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &X0, X_hex ) == 0 );

    mbedtls_mpi_swap( &X, &X );
    TEST_ASSERT( sign_is_valid( &X ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &X0 ) == 0 );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &X0 );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_shrink( int before, int used, int min, int after )
{
    mbedtls_mpi X;
    mbedtls_mpi_init( &X );

    TEST_ASSERT( mbedtls_mpi_grow( &X, before ) == 0 );
    if( used > 0 )
    {
        size_t used_bit_count = used * 8 * sizeof( mbedtls_mpi_uint );
        TEST_ASSERT( mbedtls_mpi_set_bit( &X, used_bit_count - 1, 1 ) == 0 );
    }
    TEST_EQUAL( X.n, (size_t) before );
    TEST_ASSERT( mbedtls_mpi_shrink( &X, min ) == 0 );
    TEST_EQUAL( X.n, (size_t) after );

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_add_mpi( char * input_X, char * input_Y,
                  char * input_A )
{
    mbedtls_mpi X, Y, Z, A;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z ); mbedtls_mpi_init( &A );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y, input_Y ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    TEST_ASSERT( mbedtls_mpi_add_mpi( &Z, &X, &Y ) == 0 );
    TEST_ASSERT( sign_is_valid( &Z ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Z, &A ) == 0 );

    /* result == first operand */
    TEST_ASSERT( mbedtls_mpi_add_mpi( &X, &X, &Y ) == 0 );
    TEST_ASSERT( sign_is_valid( &X ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &A ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );

    /* result == second operand */
    TEST_ASSERT( mbedtls_mpi_add_mpi( &Y, &X, &Y ) == 0 );
    TEST_ASSERT( sign_is_valid( &Y ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Y, &A ) == 0 );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z ); mbedtls_mpi_free( &A );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_add_mpi_inplace( char * input_X, char * input_A )
{
    mbedtls_mpi X, A;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &A );

    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_mpi_sub_abs( &X, &X, &X ) == 0 );
    TEST_ASSERT( mbedtls_mpi_cmp_int( &X, 0 ) == 0 );
    TEST_ASSERT( sign_is_valid( &X ) );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_mpi_add_abs( &X, &X, &X ) == 0 );
    TEST_ASSERT( sign_is_valid( &X ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &A ) == 0 );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_mpi_add_mpi( &X, &X, &X ) == 0 );
    TEST_ASSERT( sign_is_valid( &X ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &A ) == 0 );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &A );
}
/* END_CASE */


/* BEGIN_CASE */
void mpi_add_abs( char * input_X, char * input_Y,
                  char * input_A )
{
    mbedtls_mpi X, Y, Z, A;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z ); mbedtls_mpi_init( &A );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y, input_Y ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    TEST_ASSERT( mbedtls_mpi_add_abs( &Z, &X, &Y ) == 0 );
    TEST_ASSERT( sign_is_valid( &Z ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Z, &A ) == 0 );

    /* result == first operand */
    TEST_ASSERT( mbedtls_mpi_add_abs( &X, &X, &Y ) == 0 );
    TEST_ASSERT( sign_is_valid( &X ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &A ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );

    /* result == second operand */
    TEST_ASSERT( mbedtls_mpi_add_abs( &Y, &X, &Y ) == 0 );
    TEST_ASSERT( sign_is_valid( &Y ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Y, &A ) == 0 );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z ); mbedtls_mpi_free( &A );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_add_int( char * input_X, int input_Y,
                  char * input_A )
{
    mbedtls_mpi X, Z, A;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Z ); mbedtls_mpi_init( &A );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    TEST_ASSERT( mbedtls_mpi_add_int( &Z, &X, input_Y ) == 0 );
    TEST_ASSERT( sign_is_valid( &Z ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Z, &A ) == 0 );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Z ); mbedtls_mpi_free( &A );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_sub_mpi( char * input_X, char * input_Y,
                  char * input_A )
{
    mbedtls_mpi X, Y, Z, A;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z ); mbedtls_mpi_init( &A );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y, input_Y ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    TEST_ASSERT( mbedtls_mpi_sub_mpi( &Z, &X, &Y ) == 0 );
    TEST_ASSERT( sign_is_valid( &Z ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Z, &A ) == 0 );

    /* result == first operand */
    TEST_ASSERT( mbedtls_mpi_sub_mpi( &X, &X, &Y ) == 0 );
    TEST_ASSERT( sign_is_valid( &X ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &A ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );

    /* result == second operand */
    TEST_ASSERT( mbedtls_mpi_sub_mpi( &Y, &X, &Y ) == 0 );
    TEST_ASSERT( sign_is_valid( &Y ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Y, &A ) == 0 );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z ); mbedtls_mpi_free( &A );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_sub_abs( char * input_X, char * input_Y,
                  char * input_A, int sub_result )
{
    mbedtls_mpi X, Y, Z, A;
    int res;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z ); mbedtls_mpi_init( &A );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y, input_Y ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );

    res = mbedtls_mpi_sub_abs( &Z, &X, &Y );
    TEST_ASSERT( res == sub_result );
    TEST_ASSERT( sign_is_valid( &Z ) );
    if( res == 0 )
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Z, &A ) == 0 );

    /* result == first operand */
    TEST_ASSERT( mbedtls_mpi_sub_abs( &X, &X, &Y ) == sub_result );
    TEST_ASSERT( sign_is_valid( &X ) );
    if( sub_result == 0 )
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &A ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );

    /* result == second operand */
    TEST_ASSERT( mbedtls_mpi_sub_abs( &Y, &X, &Y ) == sub_result );
    TEST_ASSERT( sign_is_valid( &Y ) );
    if( sub_result == 0 )
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Y, &A ) == 0 );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z ); mbedtls_mpi_free( &A );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_sub_int( char * input_X, int input_Y,
                  char * input_A )
{
    mbedtls_mpi X, Z, A;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Z ); mbedtls_mpi_init( &A );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    TEST_ASSERT( mbedtls_mpi_sub_int( &Z, &X, input_Y ) == 0 );
    TEST_ASSERT( sign_is_valid( &Z ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Z, &A ) == 0 );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Z ); mbedtls_mpi_free( &A );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_mul_mpi( char * input_X, char * input_Y,
                  char * input_A )
{
    mbedtls_mpi X, Y, Z, A;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z ); mbedtls_mpi_init( &A );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y, input_Y ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    TEST_ASSERT( mbedtls_mpi_mul_mpi( &Z, &X, &Y ) == 0 );
    TEST_ASSERT( sign_is_valid( &Z ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Z, &A ) == 0 );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z ); mbedtls_mpi_free( &A );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_mul_int( char * input_X, int input_Y,
                  char * input_A, char * result_comparison )
{
    mbedtls_mpi X, Z, A;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Z ); mbedtls_mpi_init( &A );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    TEST_ASSERT( mbedtls_mpi_mul_int( &Z, &X, input_Y ) == 0 );
    TEST_ASSERT( sign_is_valid( &Z ) );
    if( strcmp( result_comparison, "==" ) == 0 )
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Z, &A ) == 0 );
    else if( strcmp( result_comparison, "!=" ) == 0 )
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Z, &A ) != 0 );
    else
        TEST_ASSERT( "unknown operator" == 0 );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Z ); mbedtls_mpi_free( &A );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_div_mpi( char * input_X, char * input_Y,
                  char * input_A, char * input_B,
                  int div_result )
{
    mbedtls_mpi X, Y, Q, R, A, B;
    int res;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Q ); mbedtls_mpi_init( &R );
    mbedtls_mpi_init( &A ); mbedtls_mpi_init( &B );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y, input_Y ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &B, input_B ) == 0 );
    res = mbedtls_mpi_div_mpi( &Q, &R, &X, &Y );
    TEST_ASSERT( res == div_result );
    if( res == 0 )
    {
        TEST_ASSERT( sign_is_valid( &Q ) );
        TEST_ASSERT( sign_is_valid( &R ) );
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Q, &A ) == 0 );
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &R, &B ) == 0 );
    }

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Q ); mbedtls_mpi_free( &R );
    mbedtls_mpi_free( &A ); mbedtls_mpi_free( &B );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_div_int( char * input_X, int input_Y,
                  char * input_A, char * input_B,
                  int div_result )
{
    mbedtls_mpi X, Q, R, A, B;
    int res;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Q ); mbedtls_mpi_init( &R ); mbedtls_mpi_init( &A );
    mbedtls_mpi_init( &B );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &B, input_B ) == 0 );
    res = mbedtls_mpi_div_int( &Q, &R, &X, input_Y );
    TEST_ASSERT( res == div_result );
    if( res == 0 )
    {
        TEST_ASSERT( sign_is_valid( &Q ) );
        TEST_ASSERT( sign_is_valid( &R ) );
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Q, &A ) == 0 );
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &R, &B ) == 0 );
    }

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Q ); mbedtls_mpi_free( &R ); mbedtls_mpi_free( &A );
    mbedtls_mpi_free( &B );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_mod_mpi( char * input_X, char * input_Y,
                  char * input_A, int div_result )
{
    mbedtls_mpi X, Y, A;
    int res;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &A );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y, input_Y ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    res = mbedtls_mpi_mod_mpi( &X, &X, &Y );
    TEST_ASSERT( res == div_result );
    if( res == 0 )
    {
        TEST_ASSERT( sign_is_valid( &X ) );
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &A ) == 0 );
    }

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &A );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_mod_int( char * input_X, int input_Y,
                  int input_A, int div_result )
{
    mbedtls_mpi X;
    int res;
    mbedtls_mpi_uint r;
    mbedtls_mpi_init( &X );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    res = mbedtls_mpi_mod_int( &r, &X, input_Y );
    TEST_ASSERT( res == div_result );
    if( res == 0 )
    {
        TEST_ASSERT( r == (mbedtls_mpi_uint) input_A );
    }

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_exp_mod( char * input_A, char * input_E,
                  char * input_N, char * input_X,
                  int exp_result )
{
    mbedtls_mpi A, E, N, RR, Z, X;
    int res;
    mbedtls_mpi_init( &A  ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &N );
    mbedtls_mpi_init( &RR ); mbedtls_mpi_init( &Z ); mbedtls_mpi_init( &X );

    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &E, input_E ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &N, input_N ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );

    res = mbedtls_mpi_exp_mod( &Z, &A, &E, &N, NULL );
    TEST_ASSERT( res == exp_result );
    if( res == 0 )
    {
        TEST_ASSERT( sign_is_valid( &Z ) );
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Z, &X ) == 0 );
    }

    /* Now test again with the speed-up parameter supplied as an output. */
    res = mbedtls_mpi_exp_mod( &Z, &A, &E, &N, &RR );
    TEST_ASSERT( res == exp_result );
    if( res == 0 )
    {
        TEST_ASSERT( sign_is_valid( &Z ) );
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Z, &X ) == 0 );
    }

    /* Now test again with the speed-up parameter supplied in calculated form. */
    res = mbedtls_mpi_exp_mod( &Z, &A, &E, &N, &RR );
    TEST_ASSERT( res == exp_result );
    if( res == 0 )
    {
        TEST_ASSERT( sign_is_valid( &Z ) );
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Z, &X ) == 0 );
    }

exit:
    mbedtls_mpi_free( &A  ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &N );
    mbedtls_mpi_free( &RR ); mbedtls_mpi_free( &Z ); mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_exp_mod_size( int A_bytes, int E_bytes, int N_bytes,
                       char * input_RR, int exp_result )
{
    mbedtls_mpi A, E, N, RR, Z;
    mbedtls_mpi_init( &A  ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &N );
    mbedtls_mpi_init( &RR ); mbedtls_mpi_init( &Z );

    /* Set A to 2^(A_bytes - 1) + 1 */
    TEST_ASSERT( mbedtls_mpi_lset( &A, 1 ) == 0 );
    TEST_ASSERT( mbedtls_mpi_shift_l( &A, ( A_bytes * 8 ) - 1 ) == 0 );
    TEST_ASSERT( mbedtls_mpi_set_bit( &A, 0, 1 ) == 0 );

    /* Set E to 2^(E_bytes - 1) + 1 */
    TEST_ASSERT( mbedtls_mpi_lset( &E, 1 ) == 0 );
    TEST_ASSERT( mbedtls_mpi_shift_l( &E, ( E_bytes * 8 ) - 1 ) == 0 );
    TEST_ASSERT( mbedtls_mpi_set_bit( &E, 0, 1 ) == 0 );

    /* Set N to 2^(N_bytes - 1) + 1 */
    TEST_ASSERT( mbedtls_mpi_lset( &N, 1 ) == 0 );
    TEST_ASSERT( mbedtls_mpi_shift_l( &N, ( N_bytes * 8 ) - 1 ) == 0 );
    TEST_ASSERT( mbedtls_mpi_set_bit( &N, 0, 1 ) == 0 );

    if( strlen( input_RR ) )
        TEST_ASSERT( mbedtls_test_read_mpi( &RR, input_RR ) == 0 );

    TEST_ASSERT( mbedtls_mpi_exp_mod( &Z, &A, &E, &N, &RR ) == exp_result );

exit:
    mbedtls_mpi_free( &A  ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &N );
    mbedtls_mpi_free( &RR ); mbedtls_mpi_free( &Z );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_inv_mod( char * input_X, char * input_Y,
                  char * input_A, int div_result )
{
    mbedtls_mpi X, Y, Z, A;
    int res;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &Y ); mbedtls_mpi_init( &Z ); mbedtls_mpi_init( &A );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &Y, input_Y ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    res = mbedtls_mpi_inv_mod( &Z, &X, &Y );
    TEST_ASSERT( res == div_result );
    if( res == 0 )
    {
        TEST_ASSERT( sign_is_valid( &Z ) );
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &Z, &A ) == 0 );
    }

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &Y ); mbedtls_mpi_free( &Z ); mbedtls_mpi_free( &A );
}
/* END_CASE */

/* BEGIN_CASE depends_on:MBEDTLS_GENPRIME */
void mpi_is_prime( char * input_X, int div_result )
{
    mbedtls_mpi X;
    int res;
    mbedtls_mpi_init( &X );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    res = mbedtls_mpi_is_prime_ext( &X, 40, mbedtls_test_rnd_std_rand, NULL );
    TEST_ASSERT( res == div_result );

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE depends_on:MBEDTLS_GENPRIME */
void mpi_is_prime_det( data_t * input_X, data_t * witnesses,
                       int chunk_len, int rounds )
{
    mbedtls_mpi X;
    int res;
    mbedtls_test_mpi_random rand;

    mbedtls_mpi_init( &X );
    rand.data = witnesses;
    rand.pos = 0;
    rand.chunk_len = chunk_len;

    TEST_ASSERT( mbedtls_mpi_read_binary( &X, input_X->x, input_X->len ) == 0 );
    res = mbedtls_mpi_is_prime_ext( &X, rounds - 1,
                                    mbedtls_test_mpi_miller_rabin_determinizer,
                                    &rand );
    TEST_ASSERT( res == 0 );

    rand.data = witnesses;
    rand.pos = 0;
    rand.chunk_len = chunk_len;

    res = mbedtls_mpi_is_prime_ext( &X, rounds,
                                    mbedtls_test_mpi_miller_rabin_determinizer,
                                    &rand );
    TEST_ASSERT( res == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE depends_on:MBEDTLS_GENPRIME */
void mpi_gen_prime( int bits, int flags, int ref_ret )
{
    mbedtls_mpi X;
    int my_ret;

    mbedtls_mpi_init( &X );

    my_ret = mbedtls_mpi_gen_prime( &X, bits, flags,
                                    mbedtls_test_rnd_std_rand, NULL );
    TEST_ASSERT( my_ret == ref_ret );

    if( ref_ret == 0 )
    {
        size_t actual_bits = mbedtls_mpi_bitlen( &X );

        TEST_ASSERT( actual_bits >= (size_t) bits );
        TEST_ASSERT( actual_bits <= (size_t) bits + 1 );
        TEST_ASSERT( sign_is_valid( &X ) );

        TEST_ASSERT( mbedtls_mpi_is_prime_ext( &X, 40,
                                               mbedtls_test_rnd_std_rand,
                                               NULL ) == 0 );
        if( flags & MBEDTLS_MPI_GEN_PRIME_FLAG_DH )
        {
            /* X = ( X - 1 ) / 2 */
            TEST_ASSERT( mbedtls_mpi_shift_r( &X, 1 ) == 0 );
            TEST_ASSERT( mbedtls_mpi_is_prime_ext( &X, 40,
                                                   mbedtls_test_rnd_std_rand,
                                                   NULL ) == 0 );
        }
    }

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_shift_l( char * input_X, int shift_X,
                  char * input_A )
{
    mbedtls_mpi X, A;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &A );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    TEST_ASSERT( mbedtls_mpi_shift_l( &X, shift_X ) == 0 );
    TEST_ASSERT( sign_is_valid( &X ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &A ) == 0 );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &A );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_shift_r( char * input_X, int shift_X,
                  char * input_A )
{
    mbedtls_mpi X, A;
    mbedtls_mpi_init( &X ); mbedtls_mpi_init( &A );

    TEST_ASSERT( mbedtls_test_read_mpi( &X, input_X ) == 0 );
    TEST_ASSERT( mbedtls_test_read_mpi( &A, input_A ) == 0 );
    TEST_ASSERT( mbedtls_mpi_shift_r( &X, shift_X ) == 0 );
    TEST_ASSERT( sign_is_valid( &X ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &X, &A ) == 0 );

exit:
    mbedtls_mpi_free( &X ); mbedtls_mpi_free( &A );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_fill_random( int wanted_bytes, int rng_bytes,
                      int before, int expected_ret )
{
    mbedtls_mpi X;
    int ret;
    size_t bytes_left = rng_bytes;
    mbedtls_mpi_init( &X );

    if( before != 0 )
    {
        /* Set X to sign(before) * 2^(|before|-1) */
        TEST_ASSERT( mbedtls_mpi_lset( &X, before > 0 ? 1 : -1 ) == 0 );
        if( before < 0 )
            before = - before;
        TEST_ASSERT( mbedtls_mpi_shift_l( &X, before - 1 ) == 0 );
    }

    ret = mbedtls_mpi_fill_random( &X, wanted_bytes,
                                   f_rng_bytes_left, &bytes_left );
    TEST_ASSERT( ret == expected_ret );

    if( expected_ret == 0 )
    {
        /* mbedtls_mpi_fill_random is documented to use bytes from the RNG
         * as a big-endian representation of the number. We know when
         * our RNG function returns null bytes, so we know how many
         * leading zero bytes the number has. */
        size_t leading_zeros = 0;
        if( wanted_bytes > 0 && rng_bytes % 256 == 0 )
            leading_zeros = 1;
        TEST_ASSERT( mbedtls_mpi_size( &X ) + leading_zeros ==
                     (size_t) wanted_bytes );
        TEST_ASSERT( (int) bytes_left == rng_bytes - wanted_bytes );
        TEST_ASSERT( sign_is_valid( &X ) );
    }

exit:
    mbedtls_mpi_free( &X );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_random_many( int min, data_t *bound_bytes, int iterations )
{
    /* Generate numbers in the range 1..bound-1. Do it iterations times.
     * This function assumes that the value of bound is at least 2 and
     * that iterations is large enough that a one-in-2^iterations chance
     * effectively never occurs.
     */

    mbedtls_mpi upper_bound;
    size_t n_bits;
    mbedtls_mpi result;
    size_t b;
    /* If upper_bound is small, stats[b] is the number of times the value b
     * has been generated. Otherwise stats[b] is the number of times a
     * value with bit b set has been generated. */
    size_t *stats = NULL;
    size_t stats_len;
    int full_stats;
    size_t i;

    mbedtls_mpi_init( &upper_bound );
    mbedtls_mpi_init( &result );

    TEST_EQUAL( 0, mbedtls_mpi_read_binary( &upper_bound,
                                            bound_bytes->x, bound_bytes->len ) );
    n_bits = mbedtls_mpi_bitlen( &upper_bound );
    /* Consider a bound "small" if it's less than 2^5. This value is chosen
     * to be small enough that the probability of missing one value is
     * negligible given the number of iterations. It must be less than
     * 256 because some of the code below assumes that "small" values
     * fit in a byte. */
    if( n_bits <= 5 )
    {
        full_stats = 1;
        stats_len = bound_bytes->x[bound_bytes->len - 1];
    }
    else
    {
        full_stats = 0;
        stats_len = n_bits;
    }
    ASSERT_ALLOC( stats, stats_len );

    for( i = 0; i < (size_t) iterations; i++ )
    {
        mbedtls_test_set_step( i );
        TEST_EQUAL( 0, mbedtls_mpi_random( &result, min, &upper_bound,
                                           mbedtls_test_rnd_std_rand, NULL ) );

        TEST_ASSERT( sign_is_valid( &result ) );
        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &result, &upper_bound ) < 0 );
        TEST_ASSERT( mbedtls_mpi_cmp_int( &result, min ) >= 0 );
        if( full_stats )
        {
            uint8_t value;
            TEST_EQUAL( 0, mbedtls_mpi_write_binary( &result, &value, 1 ) );
            TEST_ASSERT( value < stats_len );
            ++stats[value];
        }
        else
        {
            for( b = 0; b < n_bits; b++ )
                stats[b] += mbedtls_mpi_get_bit( &result, b );
        }
    }

    if( full_stats )
    {
        for( b = min; b < stats_len; b++ )
        {
            mbedtls_test_set_step( 1000000 + b );
            /* Assert that each value has been reached at least once.
             * This is almost guaranteed if the iteration count is large
             * enough. This is a very crude way of checking the distribution.
             */
            TEST_ASSERT( stats[b] > 0 );
        }
    }
    else
    {
        int statistically_safe_all_the_way =
            is_significantly_above_a_power_of_2( bound_bytes );
        for( b = 0; b < n_bits; b++ )
        {
            mbedtls_test_set_step( 1000000 + b );
            /* Assert that each bit has been set in at least one result and
             * clear in at least one result. Provided that iterations is not
             * too small, it would be extremely unlikely for this not to be
             * the case if the results are uniformly distributed.
             *
             * As an exception, the top bit may legitimately never be set
             * if bound is a power of 2 or only slightly above.
             */
            if( statistically_safe_all_the_way || b != n_bits - 1 )
            {
                TEST_ASSERT( stats[b] > 0 );
            }
            TEST_ASSERT( stats[b] < (size_t) iterations );
        }
    }

exit:
    mbedtls_mpi_free( &upper_bound );
    mbedtls_mpi_free( &result );
    mbedtls_free( stats );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_random_sizes( int min, data_t *bound_bytes, int nlimbs, int before )
{
    mbedtls_mpi upper_bound;
    mbedtls_mpi result;

    mbedtls_mpi_init( &upper_bound );
    mbedtls_mpi_init( &result );

    if( before != 0 )
    {
        /* Set result to sign(before) * 2^(|before|-1) */
        TEST_ASSERT( mbedtls_mpi_lset( &result, before > 0 ? 1 : -1 ) == 0 );
        if( before < 0 )
            before = - before;
        TEST_ASSERT( mbedtls_mpi_shift_l( &result, before - 1 ) == 0 );
    }

    TEST_EQUAL( 0, mbedtls_mpi_grow( &result, nlimbs ) );
    TEST_EQUAL( 0, mbedtls_mpi_read_binary( &upper_bound,
                                            bound_bytes->x, bound_bytes->len ) );
    TEST_EQUAL( 0, mbedtls_mpi_random( &result, min, &upper_bound,
                                       mbedtls_test_rnd_std_rand, NULL ) );
    TEST_ASSERT( sign_is_valid( &result ) );
    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &result, &upper_bound ) < 0 );
    TEST_ASSERT( mbedtls_mpi_cmp_int( &result, min ) >= 0 );

exit:
    mbedtls_mpi_free( &upper_bound );
    mbedtls_mpi_free( &result );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_random_fail( int min, data_t *bound_bytes, int expected_ret )
{
    mbedtls_mpi upper_bound;
    mbedtls_mpi result;
    int actual_ret;

    mbedtls_mpi_init( &upper_bound );
    mbedtls_mpi_init( &result );

    TEST_EQUAL( 0, mbedtls_mpi_read_binary( &upper_bound,
                                            bound_bytes->x, bound_bytes->len ) );
    actual_ret = mbedtls_mpi_random( &result, min, &upper_bound,
                                     mbedtls_test_rnd_std_rand, NULL );
    TEST_EQUAL( expected_ret, actual_ret );

exit:
    mbedtls_mpi_free( &upper_bound );
    mbedtls_mpi_free( &result );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_add_if( char * input_A, char * input_B,
                      char * input_S4, int carry4,
                      char * input_S8, int carry8 )
{
    mbedtls_mpi S4, S8, A, B;
    mbedtls_mpi_uint *a = NULL; /* first value to add */
    mbedtls_mpi_uint *b = NULL; /* second value to add */
    mbedtls_mpi_uint *sum = NULL;
    mbedtls_mpi_uint *d = NULL; /* destination - the in/out first operand */

    mbedtls_mpi_init( &A );
    mbedtls_mpi_init( &B );
    mbedtls_mpi_init( &S4 );
    mbedtls_mpi_init( &S8 );

    TEST_EQUAL( 0, mbedtls_test_read_mpi( &A, input_A ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &B, input_B ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &S4, input_S4 ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &S8, input_S8 ) );

    /* We only need to work with one of (S4, carry4) or (S8, carry8) depending
     * on sizeof(mbedtls_mpi_uint)
     */
    mbedtls_mpi *X = ( sizeof(mbedtls_mpi_uint) == 4 ) ? &S4 : &S8;
    mbedtls_mpi_uint carry = ( sizeof(mbedtls_mpi_uint) == 4 ) ? carry4 : carry8;

    /* All of the inputs are +ve (or zero) */
    TEST_EQUAL( 1, A.s );
    TEST_EQUAL( 1, B.s );
    TEST_EQUAL( 1, X->s );

    /* Test cases are such that A <= B, so #limbs should be <= */
    TEST_LE_U( A.n, B.n );
    TEST_LE_U( X->n, B.n );

    /* Now let's get arrays of mbedtls_mpi_uints, rather than MPI structures */

    /* mbedtls_mpi_core_add_if() uses input arrays of mbedtls_mpi_uints which
     * must be the same size. The MPIs we've read in will only have arrays
     * large enough for the number they represent. Therefore we create new
     * raw arrays of mbedtls_mpi_uints and populate them from the MPIs we've
     * just read in.
     *
     * We generated test data such that B was always >= A, so that's how many
     * limbs each of these need.
     */
    size_t limbs = B.n;
    size_t bytes = limbs * sizeof(mbedtls_mpi_uint);

    /* ASSERT_ALLOC() uses calloc() under the hood, so these do get zeroed */
    ASSERT_ALLOC( a, bytes );
    ASSERT_ALLOC( b, bytes );
    ASSERT_ALLOC( sum, bytes );
    ASSERT_ALLOC( d, bytes );

    /* Populate the arrays. As the mbedtls_mpi_uint[]s in mbedtls_mpis (and as
     * processed by mbedtls_mpi_core_add_if()) are little endian, we can just
     * copy what we have as long as MSBs are 0 (which they are from ASSERT_ALLOC())
     */
    memcpy( a, A.p, A.n * sizeof(mbedtls_mpi_uint) );
    memcpy( b, B.p, B.n * sizeof(mbedtls_mpi_uint) );
    memcpy( sum, X->p, X->n * sizeof(mbedtls_mpi_uint) );

    /* The test cases have a <= b to avoid repetition, so we test a + b then,
     * if a != b, b + a. If a == b, we can test when a and b are aliased */

    /* a + b */

    /* cond = 0 => d unchanged, no carry */
    memcpy( d, a, bytes );
    TEST_EQUAL( 0, mbedtls_mpi_core_add_if( d, b, limbs, 0 ) );
    ASSERT_COMPARE( d, bytes, a, bytes );

    /* cond = 1 => correct result and carry */
    TEST_EQUAL( carry, mbedtls_mpi_core_add_if( d, b, limbs, 1 ) );
    ASSERT_COMPARE( d, bytes, sum, bytes );

    if ( A.n == B.n && memcmp( A.p, B.p, bytes ) == 0 )
    {
        /* a == b, so test where a and b are aliased */

        /* cond = 0 => d unchanged, no carry */
        TEST_EQUAL( 0, mbedtls_mpi_core_add_if( b, b, limbs, 0 ) );
        ASSERT_COMPARE( b, bytes, B.p, bytes );

        /* cond = 1 => correct result and carry */
        TEST_EQUAL( carry, mbedtls_mpi_core_add_if( b, b, limbs, 1 ) );
        ASSERT_COMPARE( b, bytes, sum, bytes );
    }
    else
    {
        /* a != b, so test b + a */

        /* cond = 0 => d unchanged, no carry */
        memcpy( d, b, bytes );
        TEST_EQUAL( 0, mbedtls_mpi_core_add_if( d, a, limbs, 0 ) );
        ASSERT_COMPARE( d, bytes, b, bytes );

        /* cond = 1 => correct result and carry */
        TEST_EQUAL( carry, mbedtls_mpi_core_add_if( d, a, limbs, 1 ) );
        ASSERT_COMPARE( d, bytes, sum, bytes );
    }

exit:
    mbedtls_free( a );
    mbedtls_free( b );
    mbedtls_free( sum );
    mbedtls_free( d );

    mbedtls_mpi_free( &S4 );
    mbedtls_mpi_free( &S8 );
    mbedtls_mpi_free( &A );
    mbedtls_mpi_free( &B );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_sub( char * input_A, char * input_B,
                   char * input_X4, char * input_X8,
                   int carry )
{
    mbedtls_mpi A, B, X4, X8;
    mbedtls_mpi_uint *a = NULL;
    mbedtls_mpi_uint *b = NULL;
    mbedtls_mpi_uint *x = NULL; /* expected */
    mbedtls_mpi_uint *r = NULL; /* result */

    mbedtls_mpi_init( &A );
    mbedtls_mpi_init( &B );
    mbedtls_mpi_init( &X4 );
    mbedtls_mpi_init( &X8 );

    TEST_EQUAL( 0, mbedtls_test_read_mpi( &A, input_A ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &B, input_B ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &X4, input_X4 ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &X8, input_X8 ) );

    /* All of the inputs are +ve (or zero) */
    TEST_EQUAL( 1, A.s );
    TEST_EQUAL( 1, B.s );
    TEST_EQUAL( 1, X4.s );
    TEST_EQUAL( 1, X8.s );

    /* Get the number of limbs we will need */
    size_t limbs = MAX( A.n, B.n );
    size_t bytes = limbs * sizeof(mbedtls_mpi_uint);

    /* We only need to work with X4 or X8, depending on sizeof(mbedtls_mpi_uint) */
    mbedtls_mpi *X = ( sizeof(mbedtls_mpi_uint) == 4 ) ? &X4 : &X8;

    /* The result shouldn't have more limbs than the longest input */
    TEST_LE_U( X->n, limbs );

    /* Now let's get arrays of mbedtls_mpi_uints, rather than MPI structures */

    /* ASSERT_ALLOC() uses calloc() under the hood, so these do get zeroed */
    ASSERT_ALLOC( a, bytes );
    ASSERT_ALLOC( b, bytes );
    ASSERT_ALLOC( x, bytes );
    ASSERT_ALLOC( r, bytes );

    /* Populate the arrays. As the mbedtls_mpi_uint[]s in mbedtls_mpis (and as
     * processed by mbedtls_mpi_core_sub()) are little endian, we can just
     * copy what we have as long as MSBs are 0 (which they are from ASSERT_ALLOC())
     */
    memcpy( a, A.p, A.n * sizeof(mbedtls_mpi_uint) );
    memcpy( b, B.p, B.n * sizeof(mbedtls_mpi_uint) );
    memcpy( x, X->p, X->n * sizeof(mbedtls_mpi_uint) );

    /* 1a) r = a - b => we should get the correct carry */
    TEST_EQUAL( carry, mbedtls_mpi_core_sub( r, a, b, limbs ) );

    /* 1b) r = a - b => we should get the correct result */
    ASSERT_COMPARE( r, bytes, x, bytes );

    /* 2 and 3 test "r may be aliased to a or b" */
    /* 2a) r = a; r -= b => we should get the correct carry (use r to avoid clobbering a) */
    memcpy( r, a, bytes );
    TEST_EQUAL( carry, mbedtls_mpi_core_sub( r, r, b, limbs ) );

    /* 2b) r -= b => we should get the correct result */
    ASSERT_COMPARE( r, bytes, x, bytes );

    /* 3a) r = b; r = a - r => we should get the correct carry (use r to avoid clobbering b) */
    memcpy( r, b, bytes );
    TEST_EQUAL( carry, mbedtls_mpi_core_sub( r, a, r, limbs ) );

    /* 3b) r = a - b => we should get the correct result */
    ASSERT_COMPARE( r, bytes, x, bytes );

exit:
    mbedtls_free( a );
    mbedtls_free( b );
    mbedtls_free( x );
    mbedtls_free( r );

    mbedtls_mpi_free( &A );
    mbedtls_mpi_free( &B );
    mbedtls_mpi_free( &X4 );
    mbedtls_mpi_free( &X8 );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_mla( char * input_A, char * input_B, char * input_S,
                   char * input_X4, char * input_cy4,
                   char * input_X8, char * input_cy8 )
{
    /* We are testing A += B * s; A, B are MPIs, s is a scalar.
     *
     * However, we encode s as an MPI in the .data file as the test framework
     * currently only supports `int`-typed scalars, and that doesn't cover the
     * full range of `mbedtls_mpi_uint`.
     *
     * We also have the different results for sizeof(mbedtls_mpi_uint) == 4 or 8.
     */
    mbedtls_mpi A, B, S, X4, X8, cy4, cy8;
    mbedtls_mpi_uint *a = NULL;
    mbedtls_mpi_uint *x = NULL;

    mbedtls_mpi_init( &A );
    mbedtls_mpi_init( &B );
    mbedtls_mpi_init( &S );
    mbedtls_mpi_init( &X4 );
    mbedtls_mpi_init( &X8 );
    mbedtls_mpi_init( &cy4 );
    mbedtls_mpi_init( &cy8 );

    TEST_EQUAL( 0, mbedtls_test_read_mpi( &A, input_A ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &B, input_B ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &S, input_S ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &X4, input_X4 ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &cy4, input_cy4 ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &X8, input_X8 ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &cy8, input_cy8 ) );

    /* The MPI encoding of scalar s must be only 1 limb */
    TEST_EQUAL( 1, S.n );

    /* We only need to work with X4 or X8, and cy4 or cy8, depending on sizeof(mbedtls_mpi_uint) */
    mbedtls_mpi *X = ( sizeof(mbedtls_mpi_uint) == 4 ) ? &X4 : &X8;
    mbedtls_mpi *cy = ( sizeof(mbedtls_mpi_uint) == 4 ) ? &cy4 : &cy8;

    /* The carry should only have one limb */
    TEST_EQUAL( 1, cy->n );

    /* All of the inputs are +ve (or zero) */
    TEST_EQUAL( 1, A.s );
    TEST_EQUAL( 1, B.s );
    TEST_EQUAL( 1, S.s );
    TEST_EQUAL( 1, X->s );
    TEST_EQUAL( 1, cy->s );

    /* Get the (max) number of limbs we will need */
    size_t limbs = MAX( A.n, B.n );
    size_t bytes = limbs * sizeof(mbedtls_mpi_uint);

    /* The result shouldn't have more limbs than the longest input */
    TEST_LE_U( X->n, limbs );

    /* Now let's get arrays of mbedtls_mpi_uints, rather than MPI structures */

    /* ASSERT_ALLOC() uses calloc() under the hood, so these do get zeroed */
    ASSERT_ALLOC( a, bytes );
    ASSERT_ALLOC( x, bytes );

    /* Populate the arrays. As the mbedtls_mpi_uint[]s in mbedtls_mpis (and as
     * processed by mbedtls_mpi_core_mla()) are little endian, we can just
     * copy what we have as long as MSBs are 0 (which they are from ASSERT_ALLOC()).
     */
    memcpy( a, A.p, A.n * sizeof(mbedtls_mpi_uint) );
    memcpy( x, X->p, X->n * sizeof(mbedtls_mpi_uint) );

    /* 1a) A += B * s => we should get the correct carry */
    TEST_EQUAL( mbedtls_mpi_core_mla( a, limbs, B.p, B.n, *S.p ), *cy->p );

    /* 1b) A += B * s => we should get the correct result */
    ASSERT_COMPARE( a, bytes, x, bytes );

exit:
    mbedtls_free( a );
    mbedtls_free( x );

    mbedtls_mpi_free( &A );
    mbedtls_mpi_free( &B );
    mbedtls_mpi_free( &S );
    mbedtls_mpi_free( &X4 );
    mbedtls_mpi_free( &X8 );
    mbedtls_mpi_free( &cy4 );
    mbedtls_mpi_free( &cy8 );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_montg_init( char * input_N, char * input_mm )
{
    mbedtls_mpi N, mm;

    mbedtls_mpi_init( &N );
    mbedtls_mpi_init( &mm );

    TEST_EQUAL( 0, mbedtls_test_read_mpi( &N, input_N ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &mm, input_mm ) );

    /* The MPI encoding of mm should be 1 limb (sizeof(mbedtls_mpi_uint) == 8) or
     * 2 limbs (sizeof(mbedtls_mpi_uint) == 4).
     *
     * The data file contains the expected result for sizeof(mbedtls_mpi_uint) == 8;
     * for sizeof(mbedtls_mpi_uint) == 4 it's just the LSW of this.
     */
    TEST_ASSERT( mm.n == 1  || mm.n == 2 );

    /* All of the inputs are +ve (or zero) */
    TEST_EQUAL( 1, N.s );
    TEST_EQUAL( 1, mm.s );

    /* mbedtls_mpi_core_montmul_init() only returns a result, no error possible */
    mbedtls_mpi_uint result = mbedtls_mpi_core_montmul_init( N.p );

    /* Check we got the correct result */
    TEST_EQUAL( result, mm.p[0] );

exit:
    mbedtls_mpi_free( &N );
    mbedtls_mpi_free( &mm );
}
/* END_CASE */

/* BEGIN_CASE */
void mpi_core_montmul( int limbs_AN4, int limbs_B4,
                       int limbs_AN8, int limbs_B8,
                       char * input_A,
                       char * input_B,
                       char * input_N,
                       char * input_X4,
                       char * input_X8 )
{
    mbedtls_mpi A, B, N, X4, X8, T, R;

    mbedtls_mpi_init( &A );
    mbedtls_mpi_init( &B );
    mbedtls_mpi_init( &N );
    mbedtls_mpi_init( &X4 );    /* expected result, sizeof(mbedtls_mpi_uint) == 4 */
    mbedtls_mpi_init( &X8 );    /* expected result, sizeof(mbedtls_mpi_uint) == 8 */
    mbedtls_mpi_init( &T );
    mbedtls_mpi_init( &R );     /* for the result */

    TEST_EQUAL( 0, mbedtls_test_read_mpi( &A, input_A ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &B, input_B ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &N, input_N ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &X4, input_X4 ) );
    TEST_EQUAL( 0, mbedtls_test_read_mpi( &X8, input_X8 ) );

    mbedtls_mpi *X = ( sizeof(mbedtls_mpi_uint) == 4 ) ? &X4 : &X8;

    int limbs_AN = ( sizeof(mbedtls_mpi_uint) == 4 ) ? limbs_AN4 : limbs_AN8;
    int limbs_B = ( sizeof(mbedtls_mpi_uint) == 4 ) ? limbs_B4 : limbs_B8;

    TEST_LE_U( A.n, (size_t)limbs_AN );
    TEST_LE_U( X->n, (size_t)limbs_AN );
    TEST_LE_U( B.n, (size_t)limbs_B );
    TEST_LE_U( limbs_B, limbs_AN );

    /* All of the inputs are +ve (or zero) */
    TEST_EQUAL( 1, A.s );
    TEST_EQUAL( 1, B.s );
    TEST_EQUAL( 1, N.s );
    TEST_EQUAL( 1, X->s );

    TEST_EQUAL( 0, mbedtls_mpi_grow( &A, limbs_AN ) );
    TEST_EQUAL( 0, mbedtls_mpi_grow( &N, limbs_AN ) );
    TEST_EQUAL( 0, mbedtls_mpi_grow( X, limbs_AN ) );
    TEST_EQUAL( 0, mbedtls_mpi_grow( &B, limbs_B ) );

    TEST_EQUAL( 0, mbedtls_mpi_grow( &T, limbs_AN * 2 + 1 ) );

    /* Calculate the Montgomery constant (this is unit tested separately) */
    mbedtls_mpi_uint mm = mbedtls_mpi_core_montmul_init( N.p );

    TEST_EQUAL( 0, mbedtls_mpi_grow( &R, limbs_AN ) ); /* ensure it's got the right number of limbs */

    mbedtls_mpi_core_montmul( R.p, A.p, B.p, B.n, N.p, N.n, mm, T.p );
    size_t bytes = N.n * sizeof(mbedtls_mpi_uint);
    ASSERT_COMPARE( R.p, bytes, X->p, bytes );

exit:
    mbedtls_mpi_free( &A );
    mbedtls_mpi_free( &B );
    mbedtls_mpi_free( &N );
    mbedtls_mpi_free( &X4 );
    mbedtls_mpi_free( &X8 );
    mbedtls_mpi_free( &T );
    mbedtls_mpi_free( &R );
}
/* END_CASE */

/* BEGIN_CASE depends_on:MBEDTLS_SELF_TEST */
void mpi_selftest(  )
{
    TEST_ASSERT( mbedtls_mpi_self_test( 1 ) == 0 );
}
/* END_CASE */